I'm not sure I follow your idea exactly, but it sounds like you will still have an issue with the lid obstructing access, at least a little.It can absolutely be done. I can actually visualize the mechanics for one method in my head. A couple T-tracks on the bottom of the top and then a T with a cylindrical top or a notched out end of the track to allow it to pivot when fully extended would do the trick. Hidden pocket cabinet drawers do something similar.
Problem is I have no idea what the name of those parts would be to search for.
Even something that allows you to slide the lid out so it can be folded down will still have slider tracks over the opening. The t-track/ball idea you are describing won't allow for any support for the lid while opening it, will it? That wouldn't make it very user friendly.
I think at that point, you might as well just make it removeable.
What are you thinking for the top? I know you don't want to cut it and hinge it, but you can make a top that camouflages the seams for the lid.